For a stationary set S ⊆ ω1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is CHausdorff. But for every ladder E over ω1 \ S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, c...

The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced. Relationship(s) between the Bryant Schneider Group and the Smarandache Bryant Schneider Group of an S-loop are discovered and the later is found to be useful in finding Smarandache isotopy-isomorphy condition(s) in S-loops just like the formal is useful in finding isotopy-isomorphy condition(s) in loops. Some...

Let/be a locally Lipschitz function on a Banach space X, and S a subset of X. We define regular (i.e. noncritical) points for / relative to S, and give a sufficient condition for a point z e S to be regular. This condition is then expressed in the particular case when/is C1, and is used to obtain a new proof of Hoffman's inequality in linear programming.

In 1980, Bondy proved that for an integer k ≥ 2 a (k+ s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least 1 2 ((k+1)(n+ s−1)+1). This generalizes the well-known sufficient conditions of Dirac (k = 0) and Ore (k = 1). The condition in Bondy’s Theorem is not ...

The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced. Relationship(s) between the Bryant Schneider Group and the Smarandache Bryant Schneider Group of an S-loop are discovered and the later is found to be useful in finding Smarandache isotopy-isomorphy condition(s) in S-loops just like the formal is useful in finding isotopy-isomorphy condition(s) in loops. Some...

In 2 experiments we investigated the efficacy of self-paced study in multitrial learning. In Experiment 1, native speakers of English studied lists of Dutch-English word pairs under 1 of 4 imposed fixed presentation rate conditions (24 × 1 s, 12 × 2 s, 6 × 4 s, or 3 × 8 s) and a self-paced study condition. Total study time per list was equated for all conditions. We found that self-paced study ...

The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted $${\mathfrak{u}_{r,s}}({F_4})$$ as quotient Ur,s(F4) pointed, and Drinfel’d double structure under certain condition. All Hopf isomorphisms are determined, necessary sufficient condition to be ribbon algebra singled out by describ...

We analyze measures of the azimuthal asymmetry, in particular the participant harmonic moments, ε∗, in a variety of Glauber-like models for the early stage of collisions at RHIC. Quantitative comparisons indicate substantial model dependence for ε∗, reflecting different effective number of sources, while the dependence of the scaled standard deviation σ(ε∗)/ε∗ on the particular Glauber model is...

We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y′′ +(λ−q(x))2y = 0, x ∈R+ = [0,∞), subject to the spectral parameterdependent boundary condition y′(0)−(aλ+b)y(0)= 0 in the space L(R+), where a≠±i, b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that Lλ has a finite number of eigenvalues and spect...

The works of T. S. Eliot and Bob Dylan seem to flow from the same spring – an agonizing sense of the contemporary human condition and the state of society – and several critics have recently begun to observe the similarities between these two writers. Through comparative readings of T. S. Eliot’s and Bob Dylan’s earlier and later works this project investigates how their religious turn influenc...